Answer:
\(\boxed{\boxed{y\leq 2x+1}}\)
Step-by-step explanation:
If a point lies on the shaded region, then it must satisfy the inequality.
So putting the coordinates of (8, -2) in all the inequalities.
A. \(y\leq -x+4\)
\(\Rightarrow -2\leq -8+4\)
\(\Rightarrow -2
leqslant -4\)
Therefore, it does not belong to this inequality.
B. \(y\leq x-11\)
\(\Rightarrow -2\leq 8-11\)
\(\Rightarrow -2
leqslant -3\)
Therefore, it does not belong to this inequality.
C. \(y\leq -2x-3\)
\(\Rightarrow -2\leq -16-3\)
\(\Rightarrow -2
leqslant -19\)
Therefore, it does not belong to this inequality.
D. \(y\leq 2x+1\)
\(\Rightarrow -2\leq 16+1\)
\(\Rightarrow -2\leq 17\)
Therefore, it belongs to this inequality.
